Solubilities of CO2, O2 and N2 in rocket propellant 5 under low pressure

The static method of isochoric saturation was used to measure the solubilities of CO2, O2 and N2 in rocket propellant 5 (RP5) at temperatures ranging from 253.15 to 323.15 K in 10 K intervals and pressures ranging from 0 to 120 kPa. The measurement accuracy of the constructed experimental setup was verified by measuring the solubility of CO2 in water. The relative expanded uncertainty (k = 2) in the solubility data was less than 4.0%. The solubilities of CO2, O2 and N2 in RP5 increased with pressure. As the temperature increased, the solubility decreased for CO2 solubility and increased for O2 and N2. Henry's constants for the three gases in RP5 decreased over the experimental temperature and pressure ranges in the order of N2 > O2 > CO2. The measured solubilities of CO2, O2 and N2 could be fitted with a modified Krichevsky–Kasarnovsky equation, and the maximum deviation between the measured and calculated data was less than 8.04%, 7.03% and 6.18%, respectively.

Experimental apparatus and method. The isochoric saturation method was used to measure the solubilities of CO 2 , O 2 and N 2 , where the experimental system is presented in Fig. 1. The experimental apparatus consists of a gas source, a gas reservoir, a fuel tank, three pin valves, a vacuum pump, a magnetic rotor, a magnetic stirrer, a mechanical stirrer, a thermostatic bath (FDL BC-3006), three thermocouples (Model K), two pressure sensors (HSTL-800), a data acquisition system and a computer.
The water storage method was used to measure the volumes of the gas reservoir and fuel tank, including the line and valves. Disconnecting the gas reservoir from fuel tank and degassed water is injected into the gas reservoir from valve 1 until the gas reservoir is filled. The volume of gas reservoir could be measured by measuring the volume of water and repeated three times. The same method is applied to measure the volume of the fuel tank. The volumes of the gas reservoir and fuel tank are 332 ± 0.2 mL and 469 ± 0.2 mL, respectively. A thermostatic bath is used to maintain a constant temperature in the fuel tank with an error range of 0.02 K. The test range of the thermocouple is 243. 15-373.15 K with the precision of 0.02 K. The test range of the pressure sensor in the gas reservoir is 0-400 kPa with a precision of 0.1 kPa over the full pressure range.
The gas tightness of the experimental system is checked before making measurements by injecting compressed air at 300 kPa into the system; the experimental requirements are met if the pressure drop is less than 1 kPa after 24 h 18 . First, approximately 260 g of RP5 are poured into the fuel tank, and the temperature of the thermostatic bath is set to the experimental temperature. Second, the air in the gas reservoir and fuel tank is degassed by a vacuum pump, and dissolved air escapes from the fuel because of the decrease in the pressure. Third, V1 is opened, V3 is closed, and either CO 2 , O 2 or N 2 is loaded into the gas reservoir at the given temperature and pressure. Finally, V3 is opened to transfer gas into the fuel tank, and the pressure decreases as the gas dissolves The gas solubility in PR5 is presented as a mole fraction, that is, the ratio of the number of moles of dissolved gas to the total number of moles of gas and fuel. The gas solubility can be expressed as follows: where x is the mole fraction; n g,d is the number of moles of gas dissolved in fuel; and n l is the number of moles of fuel.
The fuel mole number is calculated as follows: where m l is the mass of the fuel, kg; and M l is the molecular mass of the fuel. The mole number of the dissolved gas can be expressed as follows: where ρ g,i and ρ g,f are the densities of the gas in the gas reservoir before and after transfer to the fuel tank, respectively, kg/m 3 ; ρ g,u is the density of gas in the fuel tank ullage after the transfer; and V G and V u are the volume of the gas reservoir and the fuel tank ullage, respectively, m 3 ; M g is the molecular mass of gas. The gas densities ρ g,i and ρ g,f at a given temperature and pressure can be obtained from REFPROP 9.1 21 . The fuel tank ullage can be written as follows: where V f is the fuel tank volume, m 3 ; and V l is the volume of the liquid PR5 jet fuel, m 3 .
The fuel volume can be expressed as follows: where ρ l is the density of fuel, kg/m 3 . The temperature dependence of the RP5 density affects the fuel volume calculation. Therefore, to determine the solubility accurately, the RP5 density was measured using a DA-300API electronic densitometer at temperatures ranging from 243.15 to 343.15 K and atmospheric pressure. The experimental data for the density versus temperature shown in Fig. 2 could be fitted with a linear function as follows: where T is the temperature, K.
The mole fraction x of gas dissolved in the fuel can thus be expressed as follows: where U(x) is the expanded uncertainty in the mole fraction; k is the coverage factor that can be considered as 2; u(x) is the combined standard uncertainty; and u i (x) is the uncertainty in each influencing factor. Equations (1)- (7) can be combined to express U(x) as follows: The expanded uncertainties in the measurement variables in the experiment are as follows: temperature (0.023 K), mass of RP5 (0.00002 g), pressure (0.12 kPa), volume of gas reservoir and fuel tank (0.2 mL), density of CO 2 (0.1%), density of O 2 (0.06%), and density of N 2 (0.04%). The relative expanded uncertainty in the experimental solubility data is less than 4.0% when k is 2 (In general, the value of the coverage factor k is chosen on the basis of the desired level of confidence to be associated with the interval defined by U = kuc. Typically, k is in the range 2-3. When the normal distribution applies and uc has negligible uncertainty, U = 2uc (k = 2) defines an interval having a level of confidence of approximately 95%. To be consistent with current international practice, the value of k to be used at NIST for calculating U is, by convention, k = 2 22 .).
Ethics approval. The research for this article do not include human or animal subjects.

Verification of accuracy of experimental apparatus.
To verify the accuracy of the apparatus for measuring gas solubility in RP5, the solubility of CO 2 in water was measured using the experimental system at temperatures ranging from 283.15 to 323.15 K and pressures ranging from 30 to 340 kPa; the results are shown in Table 2. Figure 3 is a comparison of the experimental data against data obtained from the literature 19 , where the average relative deviation and maximum deviation are 3.89% and 6.81%, respectively. Therefore, the experimentally obtained solubility of CO 2 in water agrees well with the literature values, and the accuracy of the apparatus meets solubility measurement requirements.

Results and discussion
Experimental solubility. The solubilities of CO 2 , O 2 and N 2 in RP5 were measured at temperatures ranging from 253.15 to 323.15 K and pressures ranging from 0 to 120 kPa. The experimental data and the expanded uncertainties in the mole fraction are listed in Tables 3, 4  The solubilities of the three gases in RP5 clearly increase with pressure. The mole fraction of CO 2 in RP5 decreases with increasing temperature. By contrast, the mole fractions of O 2 and N 2 in RP5 increase with temperature. Figure 7 shows the solubilities of CO 2 , O 2 and N 2 in RP5 at 293.15 K, where the gas solubility decreases in the order CO 2 > O 2 > N 2 at the same temperature and pressure. The solubility of CO 2 in RP5 increase faster than those of O 2 and N 2 as pressure increase, which indicates the solubility of CO 2 in RP5 is more sensitive to pressure. Solubility data analysis. Henry's law is the most commonly used correlation for evaluating the solubility of a gas dissolved in a liquid solvent. A more general form of Henry's law that accounts for pressure effects is based on a thermodynamic correlation known as the Krichevsky-Kasarnovsky equation 9,23,24 and can be expressed as follows:  Figure 3. Comparisons of the experimental solubility (mole fraction) of CO 2 in water with data from the literature. Table 3. Solubility (mole fraction) and associated uncertainty of CO 2 in RP5.  Table 4. Solubility (mole fraction) and associated uncertainty of O 2 in RP5.   is the partial molar volume of the gas in the respective solvent, L/mol; p s 2 is the saturated vapor pressure of the solvent, MPa; and R is the gas constant, 8.314 J/(mol K). The gas fugacity can be obtained using REFPROP 9.1 software 21 . The p s 2 term can neglected over the very low temperature range used in the experiment. Henry's constant and V ∞ 1 can both be expressed as functions of the temperature as follows:

T/K p/kPa x/ × 10 −3 U(x)/ × 10 −3 T/K p/kPa x/ × 10 −3 U(x)/
where A, B, a, b, and c are adjustable parameters. The modified Krichevsky-Kasarnovsky equation can be expressed as follows: www.nature.com/scientificreports/ Equation (13) can be used to obtain correlations for the individual solubilities of the three gases in RP5. Table 6 presents the adjustable parameters obtained by fitting the experimental data. Figure 8 shows the deviation between the experimental data and the value calculated using Eq. (13).
The deviation between the experimental data and the calculated values is less than 10%. The absolute average deviations (AADs) and maximum deviations (MDs) are determined to analyze the accuracy of the solubility calculated by the modified KK equation. The AAD and MD are expressed below: where x exp and x cal are the experimental and calculated mole fractions of gas in RP5, respectively, and N is the number of experimental data points.
The AADs for CO 2 , O 2 and N 2 are 2.74%, 2.25% and 2.17%, respectively. The MD values for CO 2 , O 2 and N 2 are 8.04%, 7.03% and 6.18%, respectively. Table 7 and Fig. 9 show the values of Henry's constant calculated using Eq. (11) for CO 2 , O 2 and N 2 . Henry's constant decreases as the temperature increases for O 2 and N 2 but increases with the temperature for CO 2 , that similar to the trend of CO 2 , O 2 and N 2 solubility in JP-10 in literature 18 . Henry's constant for the three gases in RP5 decreases in the order N 2 > O 2 > CO 2 , which is opposite to the trend observed for the solubility.

Conclusions
The isochoric saturation method was used to measure the solubilities of CO 2 , O 2 and N 2 in RP5 at temperatures ranging from 253.15 to 323.15 K and pressures ranging from 0 to 120 kPa. The solubility, as represented by the gas mole fraction, decreases with increasing temperature for CO 2 and increases with the temperature for O 2 and N 2 . The solubilities for the three gases decrease in the order CO 2 > O 2 > N 2 at the same temperature and pressure. The solubilities calculated using the modified KK equation are in good agreement with the experimental data. The absolute average deviations for CO 2 , O 2 and N 2 are 2.74%, 2.25% and 2.17%, respectively. Henry's constant increases with the temperature for CO 2 and decreases with increasing temperature for O 2 and N 2 , which www.nature.com/scientificreports/ represents an opposite trend to that observed for the solubility. Henry's constant for the three gases decreases in the order N 2 > O 2 > CO 2 at the same temperature.